The paper is focused on recent displacement rates in the Altai-Sayan region, obtained by hydroleveling, leveling, and satellite geodesy. Effective elastic moduli and viscosity parameters of the crust are used in the modeling of coseismic and tectonic processes. The elastic moduli are determined from measurements of periodic vertical displacements during seasonal loadings of the Sayano-Shushenskaya hydropower plant. We present the results of the modeling of coseismic displacements during the earthquakes of 10 February 2011 (M = 6.1) and 27 December 2011 (M = 6.7) in Tuva and West Sayan. The results of GPS determinations for postseismic displacements in the Chuya earthquake zone (Gorny Altai, 27 September 2003, M = 7.5) are analyzed; models for the geologic medium are selected; and its effective viscosity is estimated. The tectonic component of the recent crustal displacements in the Altai-Sayan region is defined.